`4 xx 10^(10)` electrons are removed from a neutral metal sphere of diameter 20 cm placed in air. The magnitude of the electric field (in `N C^(-1)`) at a distance of 20 cm from its centre is

Options

A. 5760
B. 1440
C. 640
D. Zero

Answer

B

Explanation

Give,
Number of electrons (n) `= 4xx10^(10)`
Diameter of sphere (D) = 20 cm
Radius of sphere (r ) `= (20)/(2)=10 cm = 0.01m`
According to question,
`E_("outside")=(q)/(4pi epsilon_(0)r^(2))`
`= ("ne")/(4pi epsilon_(0)r^(2))`
Here, `r=20xx10^(-2)m`
`= (4xx10^(10)xx1.6xx10^(-19)xx9xx10^(9))/((20xx10^(-2))^(2))`
`= (4xx1.6xx9)/(20xx20xx10^(-4))`
`= (4xx16xx9xx10^(4))/(20xx20)`
`= 16xx9xx10^(2)`
`= 144xx10^(2)=1440 NC^(-1)`